Defining some variables
Let x be the number of hours plan A takes for a single client
Let y be the number of hours plan B takes for a single client
Now, it states,
Friday, 5 people did Plan A -- 6 people did Plan B
Saturday, 3 people did Plan A -- 2 people did Plan B
Also,
Friday, total of 12 hours
Saturday, total of 6 hours
Now, given this information, you can write two different equations
5x + 6y = 12
3x + 2y = 6
Now, that we have a system of equation, 2 equations 2 unknown, we can solve for x and y
a method of doing so, (elimination method)
First, multiply the 2nd eq, by 3
9x + 6y = 18
subtract the first equation from the changed 2nd equation
9x +6y =18
5x +6y = 12
------------------
4x +0y =6
4x =6
and now we can solve for x by dividing 4 to both sides
x=6/4 = 3/2 = 1.5
now, using x, we can substitute it back into the original equations in order to determine y
Substituting it into the 1st eq,
5x + 6y = 12
substitution
5(3/2) +6y = 12
15/2 +6y =12
15/2 +6y =24/2
subtract 15/2 to both sides
6y = 9/2
divide 6 to both sides
y= (9/2)/6
y=9/12 = 3/4 =0.75
Hence
Workout Plan A takes 1.5 hours (90 minutes)
Workout Plan B take 0.75 hours (45 minutes)
